Estimating Body Mass from the Astragalus in Mammals

Estimating body mass from the astragalus in mammals

TAKEHISA TSUBAMOTO

Tsubamoto, T. 2014. Estimating body mass from the astragalus in mammals. Acta Palaeontologica Polonica 59 (2): 259–265.

Astragalar fossils have been intensively studied as an indicator of the functional morphology and phylogenetic relationships of mammals. However, relatively few studies have investigated the relationship between astragalar size and body mass, usually with a focus on a particular taxonomic group. Here, univariate and multiple regression models are used to analyze the relationship between astragalar size and body mass based on an extensive sample of extant land mammals (11 orders, 48 species, 80 individuals; body mass ranging from 18 g to 3.4 t). The analyses revealed the size of the tibial trochlea to be a better predictor of body mass than the total size of the astragalus. Based on these results, estimates of the body mass of several Paleogene land mammals were calculated and compared to those of previous studies. Thus, for example, the body mass of “Baluchitherium”, the largest terrestrial mammal known to date, was estimated at about 10–15 t.

Key words: Mammalia, astragalus, talus, regression analysis, body mass estimate, Paleogene.

Takehisa Tsubamoto [[email protected]], Great Ape Research Institute, Hayashibara Co., Ltd., 952-2 Nu, Tamano 706-0316, Japan and Hayashibara Museum of Natural Sciences, 4382-4 Shirimi, Oku-cho, Setouchi 701-4212, Japan; present address: Department of Earth Sciences, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Mat- suyama 790-8577, Japan.

Received 17 June 2011, accepted 20 September 2012, available online 21 September 2012.

Copyright © 2014 T. Tsubamoto. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

been suggested (Dagosto and Terranova 1992; Smith 2002; Introduction Mendoza et al. 2006), focusing mostly on either craniodental (Gingerich et al. 1982; Legendre 1986, 1989; Conroy 1987; The astragalus (= talus, anklebone) is a moderately compact bone forming part of the mammalian skeleton (Gray 1858). Damuth 1990; Janis 1990; Van Valkenburgh 1990; Fortelius Owing to their robust morphology, astragali are frequently 1990; Egi et al. 2002, 2004; Mendoza et al. 2006; Figuei- preserved in the fossil record, and more often found undam- rido et al. 2011) or long bone measurements (Alexander et aged than long bones, vertebrae, or fragile skulls. The mor- al. 1979; Anyonge 1993; Ruff 1990; Scott 1990; Gingerich phology of this element is highly diagnostic, easy to identify, 1990; Egi 2001; Andersson 2004; De Esteban-Triviqno et and correlates well with the behavior of the animal (e.g., al. 2008; Figueirido et al. 2011). The cross-sectional diaph- DeGusta and Vrba 2003). As a result, astragalar fossils have yseal and articular dimensions of long bones in particular been widely used as an indicator of mammalian functional seem to be good predictors of body mass for a variety of morphology, phylogenetic relationships, and taxonomy (e.g., mammals (Gingerich 1990; Ruff 1990, 2003; Scott 1990; Martinez and Sudre 1995; Nakatsukasa et al. 1997; Gebo et Anyonge 1993; Egi 2001; Andersson 2004), and are likely al. 2000; Plummer et al. 2008; Polly 2008; Dagosto et al. to perform better than either craniodental dimensions or long 2010; Parr et al. 2011). bone length measurements in the case of extinct mammals In general, the body mass of an animal strongly correlates with no close phylogenetic links or phenetic similarity to any with its ecology, physiology, functional anatomy, diet, ener- living species. getics, and life history (Peters 1983; Calder 1984; Legendre The astragalus has broad articular facets for both the tibia 1986, 1989; LaBarbera 1989; Damuth and MacFadden 1990; and fibula, and thus, like long bones, appears to be well cor- McNab 1990; Eisenberg 1990; Mendoza et al. 2004, 2005; related with body mass. However, only a few studies have Copes and Schwartz 2010), and estimates of the body mass of investigated this relationship, usually with a focus on specif- extinct species consequently form an important part of paleo- ic taxonomic groups, such as prosimian primates, artiodac- ecological analyses (e.g., Legendre 1986, 1989; Morlo 1999; tyls, catarrhine primates, pinnipeds, and hominoid primates Burness et al. 2001; Egi 2001; Smith et al. 2010). Several (Dagosto and Terranova 1992; Martinez and Sudre 1995; methodologies estimating the body mass of fossil taxa have Rafferty et al. 1995; Polly 2008; Parr et al. 2011). Because

Acta Palaeontol. Pol. 59 (2): 259–265, 2014 http://dx.doi.org/10.4202/app.2011.0067 260 ACTA PALAEONTOLOGICA POLONICA 59 (2), 2014

software; Li, linear measurements; MPE, mean percentage ABLi1 Li4 prediction error; n, sample size; P, probability; PE, prediction error; PI, prediction interval; QMLE, quasi-maximum likelihood estimator; RE, ratio estimator; SE, the smearing Li3 Li2 Li6 estimate; SEE, standard error of estimate; R, correlation co- Li5 efficient; Vo, volumes. proximal medial lateral Material and methods distal C DELi8 Li9 The core data of this study consist of the body mass (in g) and nine linear measurements (in mm) of the astragalus of 80 adult individuals, representing 48 species belonging to 11 orders of extant land mammals, and ranging from 18 g to 3.4 t (see SOM: Supplementary Online Material at http://app.pan. pl/SOM/app59-Tsubamoto_SOM.pdf). Body masses repre- Li7 sent the actual weight of each specimen, and were recorded either while the animals were still alive, or just after their plantar proximal proximal death. Owing to the limited availability of specimens for medial lateral anterior plantar plantar anterior which such data could be obtained, the dataset is somewhat anterior distal distal biased towards primates and carnivores (SOM). Nine linear measurements of the astragalus (Li1–9; Fig. 1) were taken Area: Ar1 = Li1 x Li2 Volume: Vo1 = Ar1 x Li9 to the nearest 0.01 mm using digital calipers. In addition, Ar2 = Li1 x Li3 Vo2 = Ar2 x Li9 2 3 Ar3 = Li1 x Li9 Vo3 = Ar4 x Li9 four areal (mm ) and three volumetric (mm ) variables were Ar4 = Li4 x Li5 calculated based on these measurements (Fig. 1). For the Pa- Fig. 1. Linear measurement positions on the astragalus (Li1–9) and their leogene taxa, data were derived from tables and direct mea- products (area, Ar1–4; volume, Vo1–3). The illustrations are based on a left surements of figures in the literature (Osborn 1923; Granger astragalus of Macaca fuscata (Blyth, 1875) (Primates; Cercopithecidae). and Gregory 1936; Mellett 1977; Martinez and Sudre 1995; Dorsal (= anterior) (A, B), proximal (C), lateral (D), and medial (E) views. Gebo et al. 2000), on the assumption that the fossil astragali Abbreviations: Ar1–3, cross-sectional areas of the tibial trochlea; Ar4, used represented adult individuals. Prior to analysis, all data cross-sectional area of the astragalus; Li1, transverse width of the tibial tro- were transformed to a natural logarithm. Analyses were car- chlea; Li2, proximodistal length of the lateral trochlear ridge of the tibial trochlea; Li3, proximodistal length of the medial trochlear ridge of the tibial ried out using Excel (Microsoft), JMP (SAS Institute), and trochlea; Li4, transverse width of the astragalus; Li5, proximodistal length KaleidaGraph (Synergy Software). of the astragalus; Li6, proximodistal length of the central part of the tibi- To estimate body mass (BM), least squares regression was al trochlea; Li7, transverse width between the medial and lateral trochlear used instead of major axis or reduced major axis regression, ridges of the tibial trochlea; Li8, dorsoventral thickness of the lateral part of as it can provide prediction intervals for each value (Sokal the astragalus; Li9, dorsoventral thickness of the medial part of the astrag- and Rohlf 1995; Simpson et al. 2003; Zar 2010). However, alus; Vo1–2, volume of the tibial trochlea; Vo3, volume of the astragalus. major axis and reduced major axis regression helped to deter- mine the slope (Gingerich et al. 1982; Natori 2002; Warton et of this taxonomic restriction, the results of these studies are al. 2006). Linear measurements (Li1–9), areas (Ar1–4), and difficult to apply to other mammalian groups. volumes (Vo1–3) were analyzed both together and separately This article examines the allometric relationship between using stepwise multiple regression analyses (Mendoza et al. body mass and astragalar size based on an extensive sample of 2006), with the P values to enter and leave set to 5% in JMP. extant terrestrial mammals, with the ultimate aim of providing Accurate 95 % prediction intervals (PIs) for each body mass formulae capable of estimating the body mass of a variety of estimate can be calculated following the formula of Simpson extinct taxa. As an example, the present results are applied to et al. (2003: 238). However, in the case of large sample sizes, four groups of Paleogene land mammals, and their body mass approximate PIs can be calculated more easily as ± SEE x estimates compared with those of previous studies. t(0.05)(2), d.f., where SEE is the standard error of estimate and the Institutional abbreviations.—AMNH and AM, American degrees of freedom (d.f.) = sample size (n) – 2 (Ruff 2003). In Museum of Natural History, New York, USA; FAM, Frick the case of the present analysis, the 95 % PI for 80 specimens Collection, American Museum of Natural History, New (d.f. = 78) was thus calculated as ± 1.991  SEE. York, USA; IVPP, Institute of Vertebrate Paleontology and When regression is performed using log-transformed Paleoanthropology, Beijing, China. data, a systematic detransformation bias is introduced (Smith 1993a, b). To correct for this bias, I calculated three correc- Other abbreviations.—Ar, areas; BM, body mass; CF, cor- tion factors (CFs): the quasi-maximum likelihood estimator rection factor; d.f., degree of freedom; JMP, SAS Institute (QMLE), the smearing estimate (SE), and the ratio estimator TSUBAMOTO—BODY MASS ESTIMATIONS FROM ASTRAGALI 261

(RE). The QMLE was calculated following Sprugel (1983), % the SE following Duan (1983) and Smith (1993a, b), and the 130 RE following Snowdon (1991) and Smith (1993a, b). The %SEE 120 SE value is often similar to the QMLE value, while the RE %MPE is an unrelated measure (Smith 1993a). For the purpose of 110 %MPEad-CF this analysis, I calculated an adjusted CF, consisting of the arithmetic mean of the minimum and maximum values from 100 among the former three CFs. When estimating body mass, the log value determined by the regression analysis was first 90 de-transformed to the actual value (in g), and then multiplied 80 by this adjusted CF. The degree of correlation (accuracy) between body mass 70 and astragalar size was evaluated using the coefficient of determination adjusted for the number of variables (adjusted 60 2 R ), the percent standard error of estimate (%SEE), and the 50 mean percentage prediction error (%MPE). %SEE for natural log-transformed data was calculated as %SEE = (eSEE – 1) 40  100 (Smith 1984a; Egi et al. 2002; Ruff 2003), while the percentage of prediction error of the de-transformed value 30

(%PE) was calculated as %PE = (original value – estimat- 20

Li1

Li2

Li3

Li4

Li5

Li6

Li7

Li8 ed value) / estimated value  100 (Smith 1981, 1984a, b). Li9

Ar1

Ar2

Ar3

Ar4

Vo1

Vo2 %MPE is the arithmetic mean of the absolute values of %PE Vo3 Fig. 2. Comparison of %SEE, %MPE, and %MPE arising from the for each variable calculated for each individual (Smith 1981, ad-CF 1984a, b; Dagosto and Terranova 1992). Finally, %MPE for bivariate regression analyses of the 16 astragalar measurements (Li1–9, Ar1–4, and Vo1–3). Abbreviations: ad-CF, adjusted correction factor; the values corrected using the adjusted CF was also calculat- MPE, mean percentage prediction error; SEE, standard error of estimate. ed (%MPEad-CF). measurements, with Li1 and Ar3 being more accurate than Vo1 (Table 1; Fig. 2).When all predictors were included in

Results and discussion a single multiple regression analysis, only loge(Li1) was retained in the final model. These results were corroborated The three stepwise multiple regression analyses retained by individual bivariate regressions carried out for all 16 only a single predictor per analysis: loge(Li1) for the linear, variables, which showed Li1, Ar3, and Vo1 to be the best loge(Ar3) for the areal, and loge(Vo1) for the volumetric predictors, respectively (Table 1; Figs. 2, 3). Additionally, Table 1. Results of the bivariate regression analyses of the linear, areal, and volumetric measurements. Abbreviations: N, sample size; SEE, standard error of estimate; adjusted R2, coefficient of determination adjusted by the number of variables; adjusted CF, adjusted correction factor (see text for details); %SEE, percent standard error of estimate; %MPE, mean percentage prediction error; %MPEad-CF , %MPE for the values corrected using the adjusted CF. log adjusted adjusted e N slope intercept SEE %SEE %MPE %MPE measurement R2 CF ad-CF

loge Li1 80 2.789 2.078 0.3505 0.9846 1.030 41.98 28.83 28.00

loge Li2 80 2.838 1.639 0.4560 0.9739 1.256 57.77 39.55 35.37

loge Li3 80 2.782 1.924 0.5151 0.9667 1.249 67.39 44.35 39.24

loge Li4 80 2.722 1.670 0.4417 0.9756 1.194 55.53 37.17 32.66

loge Li5 80 3.125 -0.463 0.5180 0.9664 1.345 67.86 47.48 43.49

loge Li6 80 2.868 2.333 0.8180 0.9161 1.506 126.60 93.86 71.31

loge Li7 80 2.715 3.132 0.4033 0.9796 1.045 49.68 34.01 32.57

loge Li8 80 2.802 2.562 0.5713 0.9591 1.354 77.06 52.38 48.96

loge Li9 80 2.789 2.209 0.4469 0.9750 1.207 56.35 36.49 34.59

loge Ar1 80 1.411 1.837 0.3716 0.9827 1.128 45.00 30.01 27.52

loge Ar2 80 1.399 1.968 0.3949 0.9805 1.128 48.42 32.50 30.46

loge Ar3 80 1.400 2.116 0.3580 0.9839 1.110 43.05 28.05 26.34

loge Ar4 80 1.463 0.633 0.4318 0.9766 1.250 54.00 37.57 33.36

loge Vo1 80 0.939 1.949 0.3793 0.9820 1.153 46.13 30.78 28.52

loge Vo2 80 0.934 2.032 0.3880 0.9811 1.148 47.41 31.37 29.29

loge Vo3 80 0.962 1.156 0.4142 0.9785 1.230 51.32 35.16 31.92 262 ACTA PALAEONTOLOGICA POLONICA 59 (2), 2014

A 16 All of the slopes of the major axis and reduced major axis analyses were identical to or slightly lower than the val- 14 ues inferred from the isometric hypothesis (Table 1; SOM). The adjusted R2, %SEE, and %MPE of the regressions for 12 Li1, Ar1 and Ar3 (Table 1; Fig. 2) were comparable to those rhinoceroses of previous studies focusing on craniodental or limb bone 10 measurements (Damuth 1990; Janis 1990; Scott 1990; Van Valkenburgh 1990; Dagosto and Terranova 1992; Egi et al.

BM (g) e 8 2002; Figueirido et al. 2011). Some of the measurements log illustrated in Fig. 1 were difficult to define for some taxa, 6 owing to a high degree of morphological variation. However, Li1, Li2, and Li9 were more easily determined and more 4 stable than other measurements, thus making them and their products (Ar1, Ar3, and Vo1) most suitable for this study in 2 terms of practical measurement procedures. 0123450.5 1.5 2.5 3.5 4.5 In conclusion, the width (Li1) and cross-sectional areas logeLi1 (mm) B 16 of the tibial trochlea (Ar1 and Ar3) are better predictors of body mass than indicators of the overall size of the astragalus rhinoceroses 14 (Li4, Li5, Ar4, and Vo3) (Table 1; Fig. 2). Judging from the 2 adjusted R , %SEE, %MPE, and %MPEad-CF, Li1 is as pow- 12 erful a predictor as Ar1 and Ar3 (Table 1; Fig. 2), suggesting that the width of the tibial trochlea in terrestrial mammals is 10 well constrained by body mass.

BM (g)

e 8

log

6 Application to Paleogene mammals 4 The body mass of four groups of Paleogene land mammals 2 with no close extant relatives were estimated using Li1 and 0123456789 2 Ar1 with adjusted CFs (Table 2; Fig. 4). The preferred areal logeAr1 (mm ) C 16 measure, Ar3 (=Li1  Li9), was not used here, as Li9 is often rhinoceroses difficult to obtain from the literature. However, among the in- 14 dividual bivariate regression analyses, Ar1 performed almost as well as Ar3 (Table 1; Fig. 2). 12 Largest terrestrial mammal.—Several previous studies 10 have provided estimates for the body mass of the largest terrestrial mammal known to date, the rhinocerotoid peris-

BM (g)

e 8 sodactyl “Baluchitherium” (= Paraceratherium or “Indri-

log cotherium”). The present study slightly overestimates the 6 body mass of rhinoceroses using Li1 and slightly underes- timates them using Ar1 (Fig. 3, SOM). Therefore, the mean 4 of these two estimates likely provides a better prediction for rhinocerotoids. In the case of “Baluchitherium”, this (geo- 2 metric) mean was 12.7 t, with the 95% prediction interval 0123456789ranging from 10.9–13.7 t (Table 2). It should be noted that, log Ar3 (mm2) e owing to its large size, the body mass of “Baluchitherium” Fig. 3. Scatter plots of the best-performing body mass (BM [g]) regres- could only be estimated by extrapolation, which may be sions, based on A, Li1 (mm); B, Ar1 (mm2); C, Ar3 (mm2). The black line subject to large errors (Draper and Smith 1998; Reynolds indicates the line of best fit, while the dashed lines represent the upper and 2002; Zar 2010). Nevertheless, the estimate of the present lower 95% prediction limits. study is consistent with those of Fortelius and Kappelman Ar1 was also found to be a powerful predictor, as its adjusted (1993) (11 t) and Gingerich (1990) (9–15 t), who used R2, %SEE, and %MPEs were better than those of Vo1 (Table several measurements of body length, as well as limb bone 1; Figs. 2, 3). diameters and lengths. TSUBAMOTO—BODY MASS ESTIMATIONS FROM ASTRAGALI 263

Table 2. Body mass predictions for several Paleogene mammals based on Li1 and Ar1 (= Li1  Li2), corrected using the adjusted CF (Fig. 1; Table 1). Abbreviations: BM, body mass; LPL and UPL, lower and upper 95% prediction limits. predicted LPL UPL predicted LPL UPL Li1 Li2 Species BM using using BM using using Specimen and reference (mm) (mm) using Li1 Li1 Li1 using Ar1 Ar1 Ar1 “Baluchitherium grangeri” 177.50 95.00 15.4 t 7.7 t 31.0 t 6.5 t 3.1 t 13.7 t AMNH 26387 (Granger and Gregory 1936) “Baluchitherium grangeri” 201.50 123.50 22.0 t 10.9 t 44.2 t 11.3 t 5.4 t 23.7 t AMNH 26973 (Granger and Gregory 1936) “Baluchitherium grangeri” 190.00 99.00 18.7 t 9.3 t 37.5 t 7.6 t 3.6 t 15.9 t AMNH 5209 (Granger and Gregory 1936) “Baluchitherium osborni” 185.00 132.00 17.3 t 8.6 t 34.8 t 11.0 t 5.2 t 23 t Osborn (1923: fig. 8-B1) Hyaenodon crucians 13.04 14.02 10.6 kg 5.3 kg 21.3 kg 11.0 kg 5.3 kg 23.1 kg FAM 75565 (Mellett 1977) Hyaenodon horridus 17.93 20.33 25.8 kg 12.8 kg 51.8 kg 29.2 kg 13.9 kg 61.1 kg AM 9809 (Mellett 1977) Eosimias sp. 2.81 3.48 147 g 73 g 295 g 177 g 84 g 370 g IVPP V11846 (Gebo et al. 2000)

Although the present estimate for “Baluchitherium” was trochlear width (~ Li1) and the astragalar length (~Li5). A lower than that of Economos (1981) (<20 t, based on “grav- recalculation of the body mass of these artiodactyls using itational tolerance”), the latter still lies within its maximum Li1 (~“l” in Martinez and Sudre 1995: fig. 2) resulted in upper prediction limits (Li1: 44.2 t; Ar1: 23.7 t; Table 2). By somewhat lower estimates, with the exception of Diplobune contrast, the estimate of Alexander (1989) (34 t), which was minor, which has a proximodistally much shorter propor- based on the head-body length as measured from the resto- tion of the astragalus than other artiodactyls (Martinez and ration drawings of “Baluchitherium” by Granger and Gregory Sudre 1995) (Fig. 4). However, the prediction intervals of the (1935: figs. 1, 2), lies well beyond the maximum upper pre- present analysis included the estimates of the earlier study, diction limit of Ar1, and hence might be considered unlikely. except for Doliochoerus quercyi from Pech Desse (Fig. 4),

Hyaenodontids.—Hyaenodontids are archaic carnivorous 10 000 mammals with a unique molar morphology. Here, the body based on tooth measurements mass of Hyaenodon crucians and Hyaenodon horridus was (Martinez and Sudre 1995) estimated at 11 kg and 26–29 kg, respectively (Table 2). These based on the astragalus 1000 (Martinez and Sudre 1995) values are similar to previous estimates based on head-body based on Li1 (this study), length (9 kg and 32 kg, respectively; Van Valkenburgh 1987) with 95% prediction limits and limb bone dimensions (10–25 kg and 25–60 kg; Egi 2001), but much lower than reconstructions based on the length of 100 the skull (23 kg and 150 kg; Van Valkenburgh 1987). Because head-body length is considered to be a reliable predictor of body mass (Creighton 1980; Damuth 1990; Van Valkenburgh 1990), these comparisons may indicate that the astragalus per- 10 forms well in estimating the body mass of hyaenodontids.

Estimated body mass (kg) Asian Eocene primate.—The body mass of fossil primates has been used extensively in their identification, taxonomy, 1 phylogeny, and functional morphology (e.g., Gingerich et al. 1982; Dagosto and Terranova 1992; Fleagle 1998; Gebo et al. 2000). Gebo et al. (2000) described an astragalus (IVPP 0.1 V11846) of the anthropoid primate Eosimias sp. from the Middle Eocene of Central China, and estimated the body (mean) (mean)(mean) (mean)(mean) (mean)(mean) sp. nov.sp. nov. mass of the animal to be 90–147 g based on the equations cf. (Garouillas) sp. B (mean) sp. A (mean) of Dagosto and Terranova (1992). However, the latter were (Pech Desse) exclusively derived from data on prosimian, rather than an- sp. nov. (mean) Iberomeryx minus Gelocus communis thropoid, primates. Using the present equations, I estimate Amphimeryx murinus

Diplobune minor cf. (mean) the body mass of IVPP V11846 to be 147–177 g, with a 95% Anoplotherium commune MesselobunodonMesselobunodon Anthracotherium magnum Bachitherium vireti nthracotherium valdense Dremotherium Dremotherium PI of 84–295 g (Table 2). This estimate is slightly higher, but Bachitherium curtum A Bachitherium lavocati Bachitherium Dacrytherium saturnini overall consistent, with than that of Gebo et al. (2000). Lophiomeryx chalaniati Doliochoerus quercyi

Doliochoerus quercyi Prodremotherium elongatum European Paleogene artiodactyls.—Martinez and Sudre Caenomeryx procommunis (1995) estimated the body mass of several European Paleo- Fig. 4. Comparison of body mass estimates for European Paleogene artio- gene artiodactyls based on the astragalus and m1, with their dactyls based on Li1 (this study) with those of Martinez and Sudre (1995). astragalar estimate consisting of the product of the tibial Where shown, mean estimates refer to the results of the latter study. 264 ACTA PALAEONTOLOGICA POLONICA 59 (2), 2014 which has a proximodistally long and mediolaterally narrow Dagosto, M., Marivaux, L., Gebo, D.L. Beard, K.C., Chaimanee, Y., Jae- astragalus (Martinez and Sudre 1995). ger, J.-J., Marandat, B., Soe, A.N., and Kyaw, A.A. 2010. The phylogenetic affinities of the Pondaung tali. American Journal of Physical Anthropology 143: 223–234. Dagosto, M. and Terranova, C.J. 1992 Estimating body size of Eocene pri- Concluding remarks mates: a comparison of results from dental and postcranial variables. International Journal of Primatology 13: 307–344. Tibial trochlear size is the best astragalar predictor of body Damuth, J. 1990. Problems in estimating body masses of archaic ungulates using dental measurements. In: J. Damuth and B.J. MacFadden mass, based on data from a wide variety of extant mammals, (eds.), Body Size in Mammalian Paleobiology: Estimation and Bio- and yields estimates comparable in their accuracy to those logical Implications, 229–253. Cambridge University Press, Cam- based on long bone data. When applied to a range of Paleo- bridge. gene mammals, the equations derived here yield estimates Damuth, J. and MacFadden, B.J. 1990. Introduction: body size and its esti- similar to those of previous studies, thus further supporting mation. In: J. Damuth and B.J. MacFadden (eds.), Body Size in Mam- malian Paleobiology: Estimation and Biological Implications, 1–10. the use of tibial trochlear size as a reliable indicator of body Cambridge University Press, Cambridge. mass. The present results thus have the potential to contrib- De Esteban-Triviqno, S., Mendoza, M., and De Renzi, M. 2008. Body mass ute significantly to quantitative taxonomic, ecological, and estimation in Xenarthra: a predictive equation suitable for all quadru- physiological studies of fossil land mammals, particularly pedal terrestrial placentals? Journal of Morphology 269: 1276–1293. those with no close phylogenetic links and/or similar mor- DeGusta, D. and Vrba, E. 2003. A method for inferring paleohabitats from the functional morphology of bovid astragali. Journal of Archaeologi- phological proportions to any extant species. cal Science 30: 1009–1022. Draper, N.R. and Smith, H. 1998. Applied Regression Analysis. 736 pp. 3rd edition. John Wiley & Sons, Inc., New York. Duan, N. 1983. Smearing estimate: a nonparametric retransformation meth- Acknowledgements od. Journal of the American Statistical Association 78: 605–610. Economos, A.C. 1981. The largest land mammal. Journal of Theoretical I am grateful to the following individuals involved in access to the Biology 89: 211–215. specimens used in this research: Masanaru Takai, Takeshi Nishimu- Egi, N. 2001. Body mass estimates in extinct mammals from limb bone ra, and Naoko Egi (all Primate Research Institute, Kyoto University, dimensions: the case of North American hyaenodontids. Palaeontol- Inuyama, Japan); Shin-ichiro Kawada (National Museum of Nature ogy 44: 497–528. and Science, Tokyo, Japan); and Kensuke Yasui and Keiji Matsuo- Egi, N., Takai, M., Shigehara, N., and Tsubamoto, T. 2002. Body mass esti- ka (both Toyohashi Museum of Natural History, Toyohashi, Japan). mates for Pondaung primates [in Japanese with English summary]. Pri- Thanks are also due to Masahito Natori (Okayama University of Sci- mate Research 18: 1–18. ence, Okayama, Japan), who helped with the statistical analysis. This Egi, N., Takai, M., Shigehara, N., and Tsubamoto, T. 2004. Body mass research was supported by the MEXT/JSPS Grants-in-Aid for Scien- esti mates for Eocene eosimiid and amphipithecid primates using pro- tific Research (KAKENHI, nos. 21770265 and 23370044) and the Co- simians and anthropoid scaling models. International Journal of Pri- operation Program (nos. 2011-A-3 and 2012-B-2) of Primate Research matology 25: 211–236. Institute (Kyoto University, Inuyama, Japan). Eisenberg, J.F. 1990. The behavioral/ecological significance of body size in the Mammalia. In: J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 25–37. Cambridge University Press, Cambridge. References Figueirido, B., Pérez−Claros, J.A., Hunt, R.M. Jr., and Palmqvist, P. 2011. 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